luogu P1742 最小圆覆盖

Posted 2020-12-14 with-penguin

最小圆覆盖

主要是我太菜了不会证明qwq，上面的博客讲的非常好。

主要是存代码：

#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#include<cmath>

using namespace std;

const int N=100009;
const double eps=1e-10;
int n;
struct Point
{
	double x,y;
	
	Point() {}
	Point(double X,double Y) :x(X),y(Y) {}
	Point operator + (const Point a)const { return Point(x+a.x,y+a.y); }
	Point operator - (const Point a)const { return Point(x-a.x,y-a.y); }
	Point operator * (const double a)const { return Point(x*a,y*a); }
	Point operator / (const double a)const { return Point(x/a,y/a); }
	double operator * (const Point a)const { return x*a.y-y*a.x; }
	void read() { scanf("%lf %lf",&x,&y); }
	void print() { printf("%.10lf %.10lf
",x,y); }
}a[N];

Point cross(Point p1,Point v1,Point p2,Point v2)
{
	double t=((p2-p1)*v2)/(v1*v2);
	return p1+v1*t;
}

double dis(Point a,Point b)
{
	return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
}

Point rotate_90(Point p)
{
	return Point(p.y,-p.x);
}

Point circle(Point p1,Point p2,Point p3)
{
	return cross((p1+p2)/2,rotate_90(p2-p1),(p1+p3)/2,rotate_90(p3-p1));
}

void init()
{
	scanf("%d",&n);
	for (int i=1;i<=n;i++)
		a[i].read();
}

void work()
{
	Point O(0,0);
	double r=0.;
	random_shuffle(a+1,a+1+n);
	for (int i=1;i<=n;i++)
		if(dis(O,a[i])>r+eps)
		{
			O=a[i],r=0;
			for (int j=1;j<i;j++)
				if(dis(O,a[j])>r+eps)
				{
					O=(a[i]+a[j])/2,r=dis(a[i],a[j])/2;
					for (int k=1;k<j;k++)
						if(dis(O,a[k])>r+eps)
						{
							O=circle(a[i],a[j],a[k]);
							r=dis(O,a[i]);
						}
				}
		}
	printf("%.10lf
",r);
	O.print();
}

int main()
{
	init();
	work();
	return 0;
}